The first X-Men animated series debuted on October 31, 1992 on the Fox Network as part of the "Fox Kids" Saturday morning lineup. The plot was loosely adapted from famous storylines and events in the X-Men comics, such as the Dark Phoenix Saga, Days of Future Past, the Phalanx Covenant, and the Legacy Virus. The show features a team line-up similar to that of the early 1990s X-Men comic books: the lineup largely resembles that of Cyclops' Blue Team, established in the early issues of the second X-Men comic series.
The series' first 13 episodes were notable for being possibly the first time ever that an American animated series had a full season of episodes flow one into the next, creating a single continuing narrative, something the series producers fought heavily for. However, starting with season three, most episodes (except for multi-part stories) were shown in random order.
Each episode was assigned two different numbers internally. One is for Script Order, which indicates the number assigned by the production company. The other is for Production Order, which are the official episode numbers assigned by Fox Children's Network, indicating the order in which they received the episodes. These both vary from the order in which the series actually aired after season three. According to series writer Steven Melching, the Script Order is the "best guide in terms of overall series continuity, as this is how the stories were originally envisioned to flow together."
The X-Men also appeared on Spider-Man in episodes "The Mutant Agenda" and "Mutants' Revenge". Storm later appeared in the three-part episode "Secret Wars" on the good side against the evil side. Cyclops, Wolverine, Rogue, Storm, Beast, Gambit, Jubilee, Jean Grey, and Professor X were featured as the X-Men. In the "Mutant Agenda" episode, Spider-Man's progressing neogenic mutation is making him ill and he seeks the aid of Professor Charles Xavier. In doing so he meets the X-Men but is disappointed to learn that Xavier does not 'cure' mutancy, only helps those born that way to accept and control their abilities. Wolverine in particular took issue with Spider-Man viewing his mutation as a curse. Beast however was more sympathetic to the super-hero's plight and attempted an olive branch towards him. This meeting of heroes was soon followed by a plot by Dr. Herbert Landon and the Hobgoblin to destroy mutants everywhere. But Spider-Man and the X-Men work together to defeat them and end their plot.
As of 2012, the X-Men animated show stands as the longest-running Marvel Comics based TV show, lasting for six years, with five seasons and a total of 76 episodes. The series was canceled after the episode "Graduation Day", which aired on September 20, 1997.
The following list reflects the original air dates and seasons assigned by Fox, but Marvel's official site suggests that X-Men: The Animated Series episodes should instead be viewed according to script order.

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Wolverine, Cyclops, and a core group of Marvel Comics' venerable X-Men head to Japan to prevent a mutant uprising in Marvel Anime: X-Men, a stylish revamp of the long-running franchise that's strong on action, if less so on plotting. That's an unfortunate situation, especially given the brand's history of complex and mature stor...

The X-Men, Professor X's team of mutant superheroes, races to stop Magneto and the Evil Brotherhood from destroying the human race. Also included are three classic X-Men stories. In the first, Magneto confronts the X-Men singlehandedly.

Experience new adventures and more heroic action from the company that brought you the biggest Super Hero movie of all time, Marvel's The Avengers. Iron Man, Hulk, Thor, Captain America, Hawkeye, Black Widow and the newest recruit Falcon, battle threats no single hero could vanquish in Marvel's spectacular 2-part event, Marvel's Aven...

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he made several cameo appearances throughout the series in various episodes.

Welcome, X-men fans!
I've posted all 76 episodes of "X-men: The Animated Series", plus a copy of the failed 1989 pilot "Pryde of the X-men" that I found on Google Video at the end of the blog.
All videos except for "PotXM" are linked directly from Marvel.com.
You can see for yourself here.
Also, try using Wikipedia's episode list, then search this blog by title if you have trouble finding the episode you want.
Enjoy!
PS- I also have a blog for "Spider-man: The Animated Series" at http://spidermanepisodes.blogspot.com/.